Your personal data will not be sent anywhere by the app. In more detail:

RECEIVE_BOOT_COMPLETED: If your device reboots, it has to notify this app so it can continue to monitor the network connectivity.

ACCESS_NETWORK_STATE / INTERNET: This app first checks the network using the methods provided by Android, but then also establishes a short HTTP connection (while only downloading a minimal amount of data) to make sure that the internet is really reachable. And when a crash occurs, the app will send an error report so the issue can be fixed for the next release.

CHANGE_NETWORK_STATE / CHANGE_WIFI_STATE / WRITE_APN_SETTINGS: When this app finds out that the internet is not reachable, it tries to reconnect the currently used link (wifi or mobile data). It needs the above permissions to do that.